Creep/fatigue crack growth testing,modelling and component life assessment of welds

1.1 Background to VAMAS

Versailles Agreement on Materials and Standards (VAMAS) has been active in the field of standardisation of testing and analysis of elevated temperatures fracture mechanics specimens since 1987. Between 1987–1992, a new working group, TWA11, was setup to develop and formulate a standard for a high temperature test method. This involved making recommendations for measuring the creep crack growth properties of materials and using the creep fracture mechanics parameter C ∗ in the analysis of the data. The method was restricted to creep ductile conditions. The findings were incorporated into ASTM test procedure [8] that was the first standard to deal with crack growth testing at elevated temperatures. This methodology was extended under TWA19 (1993–1998) to conditions where only limited creep deformation or otherwise creep brittle conditions were observed. It has been clear for some time that Industry needs additional justifications both in testing and analysis methods, in order to accept with further confidence the results derived in defect assessment codes. A number of European Community funded collaborative projects since 1995 have produced sizable amount of data and analysis to show the importance of testing different geometries. VAMAS TWA25 committee, established in 1999, which has had the broad aim of recommending testing, analysis and life prediction methods for assessing elevated temperature creep and creep/fatigue crack growth in metallic specimens, and ‘Feature components’ containing defects. At the present time VAMAS TWA31 is working on ‘Creep/fatigue in weldments containing residual stresses’. Therefore the plan is to further expand and improve the present recommendations for testing standards in the high temperature field.

The main objective has been to establish accurate and reliable testing methods and a unified procedure for assessing creep crack growth at elevated temperatures in industrial specimens, which contain defects. Determination of procedures for analysing the test data using fracture mechanics concepts is important and therefore the validated correlating parameters are made available in the Code of Practice (CoP) [1]. Validation of results against measurements on standard Compact Tension C(T) laboratory specimens using ASTM E1457 has been also been carried out as it indicates the effects of constraint on specimen geometry and size. There are a number of parameters such as K, linear elastic fracture mechanics, Q ∗ based on the thermally activated process [9,10] and K cmat based on creep toughness properties that are included in the CoP [1]. However recommendations are only made on the basis that they are validated with experimental data. In this paper an outline of geometries that have been tested in a number of EU programmes are identified and the differences in method of analysis using the fracture mechanics parameter C ∗ in laboratory and components will be highlighted and compared for a pipe and plate component [11–16].

1.2 VAMAS TWA31 objectives

In the past it has been shown that a collaborative effort to identify methods in testing and analysis at high temperatures has succeeded in developing standards and codes which has in turn has assisted in improving life assessment methods [1]. This programme will be extended to weldments containing extreme inhomogeneity in their material properties under VAMAS TWA31. The principal objectives of the TWA31 collaboration committee set up in September 2005 is to consider the ‘Creep/fatigue testing of weldments containing residual stress’ will be:

The new programme will build on the findings from previous work [1–7]. Described below is a short description of the different industrial life assessment procedures and methods for analysing data from different geometries and feature components which can subsequently be used in predictive lifing methods.

1.3 Background to life assessment codes

Components in the power generation and petrochemical industry operating at high temperatures are almost invariably submitted to static and/or combined cycle loading. The alloys used can vary between low carbon steels to high chrome superalloys with various alloying contents. In addition these components have welded parts which will have different alloying and microstructural properties. The failures can be due to large deformations, creep rupture and/or crack growth. The development of codes in different countries has moved in very similar direction and in many cases the methodology has been borrowed from a previously available code in another country. Early approaches to high temperature life assessment have used methodologies based on defect-free assessment codes. For example ASME Code Case N-47 [17] and the French RCC-MR [18], which have many similarities, are based on lifetime assessment of un-cracked structures. More recent methods make life assessments based on the presence of defects in the component. The more advanced codes dealing with defects over the range of creep and creep/fatigue interaction in initiation and growth of defects are the BS7910 [19], British R5/R6 [20,21], the API RP 579 [22] and the French A16 [23] which have clear similarities in terms of methodology. It is also obvious from these assessment methods that the correct evaluation of the relevant fracture mechanics parameters, for which the lifetime prediction times are dependent upon, are extremely important.

It is also evident therefore that the detailed calculation steps, which are proposed in these documents alone, do not improve the accuracy of the life prediction results. In any event as these procedures have been validated for limited sets of geometries and ‘Benchmark’ material data, their use in other operating conditions will need careful judgment. These aspects have been considered in VAMAS TWA25 in order to produce validated fracture mechanics parameters form different geometries for this purpose. The procedure highlights recommendations for improved test methods so that verifiable material properties are collected. This allows the modelling methods using standard laboratory and feature component data to be used with increased confidence in life estimation codes. This pre-standardisation work is of relevance to ASTM, ISO, ASME, API (American Petroleum Institute) and PVRC (Pressure Vessels Research Council (USA)) as well as to allow further improvements to life assessment CoP such as R5, BS7910 and A16. Clearly the recommendations resulting from this CoP will be useful for increasing confidence in defect assessment codes. In addition the similarities of the approaches in the various codes do not necessarily imply that calculations by the different methods will give the same predictions. It may be possible that under certain controlled and validated circumstance the predictions can be optimised. It is clear that a critical comparison is only possible when the same method is used on another material and condition or the same test cases are examined by the different codes.

2.1 Steady state CCG analysis

Creep crack growth rate under steady state for a creep ductile material is usually analysed using the fracture mechanics parameter C ∗ [11–16]. The derivation for C ∗ which is analogous to J is well documented [11,12] and will not be detailed in this paper. Once a steady-state distribution of stress and creep damage has been developed ahead of a crack tip, it is usually found that creep crack growth rate can be described by an expression of form [11–16]. ȧ = D · C ∗ ϕ ,(1) where D and ϕ are material constants.

Where creep dominates most often the constants in Eq. (1) are obtained from tests that are carried out on compact tension (C(T)) specimens based on the recommendations of ASTM E1457 [8] standard and hence, C ∗ is estimated experimentally from measurements of creep load-line displacement according to the experimentally determined value of C ∗ given by C ∗ = P Δ ̇ c B n ( W − a ) n n + 1 η ,(2) where Δ ̇ c is the load line displacement rate due to creep alone, B n , W and a are the specimen net thickness (accounting for side-grooves), width and crack length, respectively, n is the creep stress exponent. The geometry function η from [11,24–27] is given as η = − 1 m d m d ( a / W ) ,(3) where m is a function of collapse load of the cracked body [25]. Solutions for the η functions, in different geometries, based on analytical solutions (limit load analyses) and finite element calculations are available [25]. From Eq. (2) therefore providing that the displacement rates can be measured it is possible to simply derive C ∗ experimentally [26,27] for subsequent use in Eq. (1).

The data obtained from C(T) specimens using Eq. (1) is considered as ‘benchmark’ material data for creep crack growth properties of the materials in the same way as creep strain rate and rupture for uniaxial creep tests. These data can be employed directly in crack initiation and growth models described in the different codes [19–23] to estimate residual lives in components. For components such as pipes and plates, on the other hand, C ∗ must be determined from finite element analysis or reference stress methods. For this the reference stress procedure is adopted in line with that used in the defect assessment codes [19–23]. With this approach C ∗ is expressed approximately as [11]: C ref ∗ = σ ref · ε ̇ ref · ( K σ ref ) 2 ,(4) where ε ̇ ref is the creep strain rate at the appropriate σ ref for the component and K is the stress intensity factor corresponding to the applied loading. When the creep strain rate ε ̇ at an applied stress σ can be described in terms of the Norton creep law [11]: ε ̇ = A · σ n ,(5) where A and n are material constants at constant temperature. Thus, Eq. (4) can be rewritten as: C ref ∗ = A · σ ref n − 1 · K 2 .(6) The typical value for n is between 5 and 12 for most metals. In addition, the concept of the average creep rate, ε ̇ Ave , obtained directly from rupture data, has been used to account for all three stages of creep as an approximate method for estimating the average creep rate ε ̇ Ave as shown and defined by ε ̇ Ave = ε f t R = ε ̇ 0 · ( σ σ 0 ) n Ave = A Ave · σ n Ave ,(7) where σ is the applied stress, ε f is the uniaxial failure strain, t R is the time-to-rupture and A Ave , n Ave , σ 0 and ε ̇ 0 are material constants.

When a structure containing a defect is first loaded the stress distribution is given by the elastic K-field or the elastic–plastic J-field. Therefore, time is required for the stresses to redistribute to the steady-state creep stress distribution controlled by C ∗ . During this period, transient conditions exist which are not uniquely defined by C ∗ . In addition, a period of time is needed for creep damage to develop around the crack tip [11]. Furthermore due to the practical limitations of crack detection equipment, the initiation of crack growth is difficult to determine precisely. Typically, this ranges between an extension Δ a of between about 0.1 and 0.5 mm depending on component and crack dimensions. For laboratory specimen such as CT, ASTM E1457 [8] identifies an extension of 0.2 mm to cover the entire transition time to steady state conditions and this distance also takes into account the resolution of crack monitoring equipment. However, in order to increase the confidence in the crack measurement of the different components, it has been determined, in this present work, that Δ a = 0.5 mm was the best value to choose to compare both the CT data and the semi-elliptical defects in the pipes and plates.

From Eq. (1) it may be expected that the time, t i , to initiate a crack extension of Δ a can be expressed by: t i = D i · C ∗ ϕ i ,(8) where D i and ϕ i are material constants. For steady-state cracking D i is expected to be given approximately by Δ a / D with ϕ i = − ϕ and hence Eq. (8) can be re-written as follows [26,27]: t i = Δ a D · C ∗ − ϕ i .(9) This equation assumes that the entire initiation period is governed by steady-state C ∗ . This cannot be expected to be true during at least part of the initiation period t i . The applicability of the equation has been examined for the pipes and plates [1] in the same as has been done for crack growth.

For fatigue crack growth it is assumed that the mechanism is time and temperature independent and K or J dominates at the crack tip. At room temperature under cyclic loading conditions, crack propagation usually occurs by a fatigue mechanism where the Paris Law can describe crack growth/cycle ( d a / d N ) f in terms of stress intensity factor range Δ K by ( d a / d N ) f = C ′ Δ K m ′ ,(10) where d a / d N is fatigue crack growth rate per cycle, C ′ and m ′ are material dependent parameters, which may be sensitive to the minimum to maximum load ratio R of the cycle. The procedure for fatigue crack growth testing is well known [28]. However for low frequency dwell periods where creep dominates the parameter of choice would be the same as for static creep testing such as C ∗ [11,29].

At elevated temperatures combined creep and fatigue crack growth may take place. However in most cases fatigue dominates at higher frequencies ( f > 1 Hz ) and creep dominates at lower frequencies and dwell periods ( f < 0.1 Hz ). There is a substantial number of references in relation to this methodology [28–31] which linearly adds the creep and fatigue components of failure. In most cases the total crack growth crack growth calculations under cyclic loading can be described as ( d a / d N ) = ( d a / d N ) c + ( d a / d N ) f ,(11) where this linear summation combines creep and fatigue components. This can be refined using the method given in the British Energy’s R5 Procedure [20].

Total crack growth per cycle, ( d a / d N ) , can be described by Eqs (1), (10). It can be shown that a simple cumulative damage law can be applied to describe creep/fatigue interactions [29]. Fatigue analysis is usually conducted by using the linear elastic K parameter [1,8] and the creep portion can be described by C ∗ [29].

As a result of EU collaborative programmes [2–7] especially in HIDA [3], LICON [4] and CRETE [5] tests were performed on a number of fracture mechanics geometries. The VAMAS procedure [1] uses the information provided by these programmes to identify and catalogue six specimen geometries, as given in Table 1, that have been verified for the purpose of creep and creep/fatigue crack growth and initiation testing and are comparable to C(T) test data [26]. Abbreviations denoting the specimen geometries are also given in Table 1. The choice of specific specimens does not mean that other geometries should not be used for testing but that they would need validation before their inclusion in the procedure. Detailed dimensions, machining instructions methods of setting up and limits of testing accuracies are described in the procedure. Figure 1 shows the schematic drawings of the six fracture mechanics geometries showing the loading directions, and the load-line Δ LLD and crack Mouth opening Δ CMOD measuring positions.

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Fig. 2.

(a) Example of normalised crack length versus time data and (b) comparison of the creep crack growth rates with C ∗ for different geometries with the C(T) databand, for Δ a ⩾ 0.2 mm , in 316H stainless steel at 550°C.

An example of data obtained and analysed from these specimens are shown in Fig. 2. Figure 2(a) shows the normalised crack length versus time for the different geometries and Fig. 2(b) shows the correlation of the data when compared to a C(T) databand of the same 316 type stainless steel material. This suggests that for the range of sizes and geometries used the crack growth data obtained is comparable to within the inherent scatter of data.

Feature type specimens, which can represent component related geometries, were also tested for verification and validation in different collaborative programme [3]. A schematic of these types of specimens are shown in Fig. 3. These consist of pipes, plates and notched bar cracked specimens. The testing of such specimens is costly and difficult and is not recommended as a routine procedure for deriving data but they can be used to validate the laboratory data in comparison to components.

Analysis of component or feature component testing was an important part of VAMAS TWA25 procedure [1]. It has been shown previously that although different codes employ Eqs (5)–(7), often different formulae are used to evaluate K and σ ref . Greater sensitivity of C ∗ and cracking rate to reference stress than to K is expected from Eq. (5) since ϕ in Eq. (1) is close to one, and typically n ≫ 1 and evidence of this has been demonstrated previously [31]. It has also been previously demonstrated that ‘global’ collapse solution represent best the cracking behaviour in pipe components [1]. Some examples of the comparisons of data for the plate and pipe with C(T) specimens are given in the next section to highlight the analysis and the difficulties that exist in producing and treating the data from feature test.

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Fig. 3.

Feature geometries showing a pipe, pipe-bend notched bar with circumferential crack and plate under bending and tension feature specimens showing crack and loading positions [1]. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/SFC-150176.)

Furthermore since it has been shown [31] that there is no absolute correct solution for reference stress in components and that in order to get an overall agreed definition compromises have to be made. It may be possible by using detailed FE analysis of the geometry in 3D and the right boundary conditions and material properties to improve the solutions in the future. But for the present it is more important to be able to compare inter-laboratory data and reach definitive comparison with the results. Hence the recommendations in the CoP [1] of specific formulae for evaluating the C ∗ parameter is of importance since this will reduce the uncertainty when data are compared between different laboratories.

For plates there exist several reference stress solutions [19–23] which use Eqs (4), (6) to derive C ∗ . However in the VAMAS procedure [1] one reference stress solution is chosen. It has been shown that for small partially penetrating defects in plates subjected to combined tension and bending loading, these reference stresses can significantly over-estimate creep crack growth rates. Therefore a recommended reference stress, which is based on a global collapse mechanism is expressed as follows: σ ref Plate = ( σ b + 3 · γ · σ m ) + { ( σ b + 3 · γ · σ m ) + 9 · σ m 2 · [ ( 1 − γ ) 2 + 2 · γ · ( α − γ ) ] } 1 / 2 3 · { ( 1 − γ ) 2 + 2 · γ · ( α − γ ) } ,(12) where γ = ( a · c ) / ( W · l ) and α = a / W . In these equations, a is crack depth, c is half crack length at the surface, W is the thickness of the plate and l is the half-width of the plate, respectively.

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Fig. 4.

Effect of static and cyclic loading on crack growth rate, for 316LN at 650°C for (a) C(T) specimens [3] showing the range of data scatter and (b) comparison of plate crack growth data at different frequencies with the same C(T) databand as in Fig. 5(a).

Figure 4 gives and example of comparing the effects of frequency and the plate geometry for a 316LN type stainless steel tested at 650°C [3]. Figure 4(a) highlights that for low frequencies the crack growth data for this steels lies within the scatter of the static load data, suggesting that the cracking is time dependent and due to creep at low frequencies. Figure 4(b) compared the same databand with data from plate tests. In this case there is a clear difference between negative R-ratios and the rest of the cyclic test data of the plate lying at the upper and lower bounds of the C(T) databand respectively. This suggests that caution would be needed in using standard laboratory tests to predict component behaviour where negative R-ratios are present. It is clear therefore that a comprehensive validation of different materials, geometries and loading conditions would be needed to validate the procedure fully.

In the same way as the plates Eqs (4), (6) are used to derive C ∗ for pipe geometries. For a range of pipes also exist to derive K and reference stress. It has been shown that solutions for K due to Raju and Newman [32] and the ‘global’ collapse solution for the reference stress are best to estimate C ∗ in the analysis for pipes. ‘Global’ solutions of reference stress are based on the collapse of the entire cross-section at the site of a defect. For a semi-elliptical axial defect in a pipe subjected to an internal pressure p, R6 [21] gives the reference stress as: σ ref Pipe = p 1 R e − a · bate ( a , c ) + ln ( R e − a R i ) ,(13) where bate ( a , c ) is given by: bate ( a , c ) = a 1 + 1.61 · c 2 [ ( R e − a ) · a ] ,(14) where bate ( a , c ) is function of dimensions, a is crack depth, c is half crack length at the surface and R i and R e are the internal and external radii of the pipe, respectively.

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Fig. 5.

(a) Comparison of welded and parent crack growth rate for P22 steel tested at 565°C, and (b) comparison of crack growth versus C ∗ for P22 CT and pipe specimens with C(T) databand (Fig. 6(a)) showing the effects of geometry constraint on crack growth [3]. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/SFC-150176.)

Figure 5 gives an example of comparison of crack growth analysis of the C(T) and pipes geometries in both parent and weld P22 steel tested at 565°C. Figure 5(a) shows little difference between parent and heat affected zone (HAZ) region tests for the C(T) P22 specimens. On the other hand Fig. 5(b), for the pipe test whilst not showing a noticeable difference between parent and HAZ cracking it does show an effect due to geometry when compared with the databand of Fig. 5(a). This could be due to constraint as well as the fact that derivation of data from pipe test are much more difficult than for standard C(T) specimen [8,31]. This highlights the fact that more tests would be needed to improve the validation of laboratory data with component data.